An intrinsic problem that is associated to any rkHs is a description for \(M_z\) -invariant closed subspaces. The first of such a characterization is due to Beurling [1]} in the case of \(M_z\) -invariant clsoed subspaces of \(H^2(\) . This remarkable result holds true even for \(A^2(\)  as proved by Aleman, Richter and Sundberg in [2]} and also for \(\mathcal {D}(\)  as proved by Richter (see [3]}). In particular, Beurling's theorem extracts a significant information about the subspace.
